SPECIAL SECTION ON ENERGY EFFICIENT COMMUNICATIONS WITH ENERGY HARVESTING AND WIRELESS POWER TRANSFER

Received September 2, 2017, accepted September 26, 2017, date of publication September 29, 2017, date of current version November 7, 2017.

Digital Object Identifier 10.1109/ACCESS.2017.2757947

Wireless Energy Harvesting by Direct Voltage Multiplication on Lateral From a Suspended Layer

LOUIS WY LIU 1, QINGFENG ZHANG 1, YIFAN CHEN2, MOHAMMED A. TEETI1, AND RANJAN DAS1,3 1Electrical and Electronics Engineering Department, Southern University of Science and Technology, Shenzhen 154108, China 2School of Engineering, University of Waikato, Hamilton 3240, New Zealand 3School of Engineering, IIT Bombay, Mumbai 400076, India Corresponding author: Qingfeng Zhang ([email protected]) This work was supported in part by the Guangdong Natural Science Funds for Distinguished Young Scholar under Grant 2015A030306032, in part by the Guangdong Special Support Program under Grant 2016TQ03X839, in part by the National Natural Science Foundation of China under Grant 61401191, in part by the Shenzhen Science and Technology Innovation Committee funds under Grant KQJSCX20160226193445, Grant JCYJ20150331101823678, Grant KQCX2015033110182368, Grant JCYJ20160301113918121, Grant JSGG20160427105120572, and in part by the Shenzhen Development and Reform Commission Funds under Grant [2015] 944.

ABSTRACT This paper explores the feasibility of wireless energy harvesting by direct voltage multiplication on lateral waves. Whilst free space is undoubtedly a known medium for wireless energy harvesting, space waves are too attenuated to support realistic transmission of wireless energy. A layer of thin stratified dielectric material suspended in mid-air can form a substantially less attenuated pathway, which efficiently supports propagation of wireless energy in the form of lateral waves. The conductivity of the suspended dielectric layer does not appear to be a critical factor rendering propagation of lateral waves impossible. In this paper, a mathematical model has been developed to simulate wireless energy harvesting over a suspended layer of stratified dielectric material. The model has been experimentally verified with the help of a novel open-ended voltage multiplier designed to harvest energy from ambient electromagnetic fields.

INDEX TERMS Energy harvesting, stratified ground, , Avremenko diode configurations, trapped waves, transverse magnetic modes, TM modes, TEM modes, Zenneck Waves, lateral waves, ground waves.

I. INTRODUCTION Throughout the last century, there have been many unsuc- Whilst many researchers of this date are still struggling to cessful attempts to use Zenneck’s version of surface waves to transmit wireless energy over just a few meters by mag- explain Marconi’s work [8]–[12]. The absence of an appro- netic coupling, the feasibility of long range wireless energy priate theory for surface waves or their derivatives does not harvesting has long been proven beyond any doubt by necessarily mean that Marconi’s achievement in long range Marconi [1]–[3]. In one of Marconi’s early experiments, wireless power transfer (WPT) has to be erased from history. wireless energy was successfully and safely transmitted Towards the end of the last century, Wait came forwards with and harvested over 2 miles of a hilly area by grounding a concept of trapped surface waves in a stratified ground [13]. and lengthening monopole as a way to reduce Trapped surface is an evanescent wave propagating by the aperture size of the antenna. Marconi concluded from successive internal reflections due to an incident electromag- his first breakthrough experiment that his antenna radi- netic wave striking at an interface with an angle greater than ated vertically polarized waves that could travel the critical angle. However, the energy from trapped surface distances much longer than other conventional counter- waves has not been found to be significant in many situa- parts. Later, he even achieved non-line-of-sight (NLOS) tions [14]. In the same decade, another much more promising propagation of wireless power across the Atlantic concept known as lateral wave was used by King to explain Ocean [4]–[7]. the dominant electromagnetic waves propagating over the

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surface of a stratified ground [15]. This lateral wave is a TABLE 1. Differences between space waves and surface waves. vertically polarized electromagnetic wave on the top surface of the ground as a result of an incident electromagnetic wave striking the air-ground interface from below at exactly the critical angle [16], [17]. For an interface between two different dielectric media, the critical angle is only applica- ble to the dielectric medium with a higher . To excite this lateral wave, it is logical to bury the lower end of transmitting and receiving aerials into the dielectric layer with a higher refractive index in much the same way as grounding a in Tesla’s or Marconi’s work [2], [16]–[18]. In fact, the vertically polarized as referred by Marconi or ground current referred by is most likely equivalent to the lateral wave referred by King, Tamir and many other researchers in the field of wireless energy harvesting. Ironically, most of the recently published systems for WPT are still based on space waves, including the magnetic cou- pled waves for near field applications and the Hertzian radio waves for far field applications. Space waves are known to be inefficient because a significant amount of energy in an unguided space wave is lost by radiation. On the other hand, transmitting a large electric power through free space will directly impose interference to the present communica- tion systems. Another little-known fact is that an extremely low- space waves can potentially trigger release of toxins from microvesicles of monocytic leukaemia cells [19]. The authors believe that delivering electric power through the physical ground, ocean or the wall of a building is a far more logical solution. In this article, the feasibility of wireless energy harvesting by voltage multiplication on lateral waves is explored by an unconventional means. Instead of transmitting a wireless energy through a thick layer of a concrete ground, we extend the original idea of Tesla’s or Marconi’s to harvest a wireless energy from a thin layer of dielectric material suspended in mid-air. We begin our presentation by formulating a math- ematical model of electromagnetic waves associated with a dielectric layer suspended in mid-air. The theoretical work will be substantiated with the results of WPT experiments based on a little known open-ended voltage multiplier. Applications of lateral-wave-based WPT will be explored in areas of wireless communication according to the well understood differences between surface waves and space waves as summarized in Table 1. waves and lateral waves. The existence of trapped surface waves is possible if and only if the suspended layer of dielec- II. ELECTROMAGNETIC MODELING OF A SUSPENDED tric material is sufficiently thick, perhaps, thicker than half of LAYER OF A DIELECTRIC MATERIAL the . To rule out the possibility of trapped surface While stratified ground with a perfect conducting bot- waves being present to a significant extent, we have chosen to tom plane as a medium for transmission of trapped study the suspended dielectric layer with a thickness substan- surface waves and lateral waves has been extensively tially smaller than half of the wavelength. Examples of this studied [13]–[15], [20], the results of our investigation reveal stratified ground with imperfectly conducting bottom plane that a suspended layer of dielectric material can be modeled include a table top, an iron-reinforced concrete wall or any as a 4-layered stratified ground with imperfectly conduct- suspended dielectric layer coated with an oxide. ing ground. The stratified ground with imperfectly conduct- Fig. 1 illustrates how a suspended dielectric layer can be ing ground can support propagation of both trapped surface visualized as a conventional four-layered stratified ground

21874 VOLUME 5, 2017 L. W. Liu et al.: Wireless Energy Harvesting by Direct Voltage Multiplication on Lateral Waves

layer j defined as q = 2 − 2 γj kj λ , (3) Q, which is the reflection coefficient of the half-space due to the multi-layered configuration, can be expressed as:

2 k0 γ0 − Zs = − ωµ0 Q 2 , (4) k0 γ + Zs 0 ωµ0

In (4), Zs represents the surface impedance for the 4-layered stratified ground configuration as defined in [15]: FIGURE 1. Configuration of wireless power transfer involving a dipole vertically mounted on the surface of a suspended dielectric layer.  2 2 2 − 2  γ1µ0ωk1 γ2 k3 tan (γ2l2) i γ2γ3k2  4   γ1γ3k2 tan (γ1l1) tan (γ2l2)  +γ1µ0ω 2 2 +iγ1γ2k k tan (γ1l1) with imperfect conducting plane at the bottom. This dielectric Z = 2 3 . (5) s  4 − 2 2  configuration is similar to the 4-layered ground that has iγ1γ3k2 tan (γ2l2) γ1γ2k2 k3 2 + 2 2 3 already been considered in other studies [14], [20], with k1  γ2 k1 k3 tan (γ1l1) tan (γ2l2)  + 2 2 an exception that the bottom layer in the present work is iγ2γ3k1 k2 tan (γ1l1) a layer of air with an extremely small conductivity. The The first and second integral terms on the right side of (2) relative of layers 0, 1, 2 and 3 are respectively represents the direct space wave and the reflected space wave ε0, ε1, ε2 and ε3, where ε0 = ε3=1. The thicknesses of respectively. These two integral terms have been evaluated by layer 0 and layer 3 is assumed to be infinity. The distance King et al. [15]: between the transmitting antenna and the receiving antenna iµ Z ∞ is denoted by r. Layer 1 and layer 2, respectively, have a 0  | − |  −1 2 exp (iγ0 z d ) γ0 J1 (λr) λ dλ finite thickness l1 and l2. The length of the vertically mounted 4π 0 ! dipole is of approximately 1/4 -wavelength of the chosen iµ  ρ  ik 1 = − 0 ik R 0 − operating frequency. The apparent pathway of a lateral wave exp ( 0 1) 2 , (6a) 4π R1 R1 R is highlighted in red. As shown in Fig. 1, the deeper the dipole 1 iµ Z ∞ is submerged underneath the top surface of layer 1, the more 0  +  −1 2 exp (iγ0 (z d)) γ0 J1 (λr) λ dλ energy radiated out from the base of the vertical dipole will be 4π 0 ! striking the interface between air and layer 1 at critical angle iµ  r  ik 1 = − 0 ik R 0 − exp ( 0 2) 2 . (6b) and the more energy will be converted into a lateral wave. 4π R2 R2 R In Fig. 1, the wave numbers in all the layers are: 2 √ The third integral term represents a superimposition of the = = k0 k3 ω µ0ε0 (1a) trapped and the lateral wave. This integral term r  σj  is complex and it has to be resolved by Cauchy Riemann’s kj = ω µ ε0εrj + i , with j = 1, 2 (1b) ω residue theorem. To begin with, Zs in (5) is then substituted where ω is the angular in radian, µ and µ0 are into (4). The quantity (Q+1) in the third integral of (2) is then respectively the permeabilities of layer j and free space and symbolically derived into the form of a rational expression, σj is the conductivity of layer j. using MATLAB or a similar mathematical analysis tool: Using modal analysis, the time-varying transverse mag- A (λ) (Q + 1) = 2ik2γ , (7) netic field in the multi-layered ground can be modeled in 0 1 q (λ) frequency domain and can be expressed as in (2) [14], [20]. where the nominator A(λ) is given by: The formula given in (2) as follows is applicable to both the transmitting and receiving antennas. h 2 2 2 4 i A (λ) = −i tan (γ2l2) γ2 k3 k1 − iγ1γ3k2 tan (γ1l1) Z ∞ iµ0 − h i B (ρ, z) = exp (iγ |z − d|)γ 1J (λr) λ2dλ 2 2 2 φ 0 0 1 + γ2k2 γ3k1 i + γ1k3 tan (γ1l1) , (8a) 4π 0 iµ Z ∞ + 0  +  −1 2 and the denominator q(λ) is: exp (iγ0 (z d)) γ0 J1 (λr) λ dλ 4π 0 Z ∞ q(λ) iµ0   −1 + − (Q + 1) exp (iγ0 (z + d)) γ " 2 4 + 2 4 2 # 4π 0 γ0γ1γ3k1 k2 i γ0γ2 k1 k3 tan (γ1l1) 0 = tan (γ2l2) 2 + 2 2 4 + 2 2 2 2 × J1 (λr) λ dλ, (2) γ1 γ3k0 k2 tan (γ1l1) i γ1γ2 γ0 k1 k3 i  2 2 2 4  γ k k tan (γ1l1) i + γ0γ3k tan (γ1l1) i where λ is the wavelength, J1(...) is the Bessel function of + γ k2 1 0 3 1 . (8b) 2 2 −γ γ k2k2 − γ γ k2k2 the first kind of order 1 and γj is the propagation constant at 0 1 3 1 1 3 0 1

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When a dielectric layer is suspended in mid-air, we have to a trapped surface wave if the suspended dielectric layer k3 = k0. Thus. (8a) and (8b) can be simplified as: is too thin. However, the upper and lower interfaces of the dielectric layer remain reflective even in the absence of any 2  2 2  A (λ) = γ2k1 γ2k0 tan (γ2l2) + γ1k2 i trapped surface waves. If an incoming electromagnetic wave   strikes at either interface of an extremely thin dielectric layer − γ k2 tan (γ l ) γ k2 − ik2γ tan (γ l ) , (9a) 1 2 1 1 2 0 2 0 2 2 at critical angle, the electromagnetic energy will be forced to " 2 2 4 + 2 4 2 # propagate along the upper and lower interface in the form of γ0 γ1k1 k2 i γ0γ1 k2 k0 tan (γ1l1) q(λ) = tan (γ2l2) a lateral wave with an extremely high current density. γ 2γ k2k4 tan (γ l ) i + γ γ 2k4k2i 2 0 0 1 1 1 1 2 0 1 Mathematically, this lateral wave can be derived by eval-  γ 2k4 tan (γ l ) i + k4γ 2 tan (γ l ) i  + γ k2 0 1 1 1 0 1 1 1 . uating the last summation term of (11), which is due to the 2 2 − 2 2 2γ0γ1k0 k1 integral contribution of all the branch cuts in the complex (9b) plane. The contribution of the integral term along the branch cuts at k1 is essentially zero. Layer 3 can be regarded as an Using the relationship between Bessel function and the imperfectly conducting layer. Since the lateral wave from Hankel function, the third term of (2) can be rewritten as the interface between layer 3 and layer 2 has to propagate follows: through a much longer and more attenuated pathway before iµ Z ∞ 0 − + +  −1 2 reaching the receiver, the contribution of the branch cut k3 to (Q 1) exp (iγ0 (z d)) γ0 J1 (λr) λ dλ 4π 0 the receiving end can be assumed to be negligible although iµ k Z ∞ A (λ)  this assumption can be invalid if the suspended dielectric = 0 0 + −1 (1) 2 exp (iγ0 (z d)) γ0 H1 (λr) λ dλ 4π −∞ q (λ) layer is too thin. The main contribution to the lateral wave (10) is due to the branch cut at k0. This integral term needs to be resolved using Fresnel integral and a complementary error- (1) where H1 (...) is the first order Hankel function of first kind. function. The approach proposed in [20] is adopted. To start By Cauchy-Riemann’s residue theorem, (10) can be further with, the following approximation is made: expressed as (11), as shown at the bottom of this page, for λ = k (1 + iτ) (13a) j = 0, 1, 2, .. 0 s 2   3π    (1) ≈ − − 2 III. LATERAL WAVES IN A SUSPENDED LAYER H1 (λr) exp i k0r exp k0rτ πk0r 4 OF LOSSY DIELECTRIC The first summation term on the right side of (11) refers to (13b) q the trapped surface wave due to the poles of the integrand ≈ = 2 − 2 = γj γj0 kj k0 , for j 1, 2 (13c) in (10), λk . The poles can be numerically resolved by equat- ing q(λ) in (8b) to zero. As has been pointed by Li [20], Finally, the expressions in (13a), (13c) and (13b) are sub- (11) will yield n+1 poles between ki and ki+1 if the electrical stituted into the large integral term of (11) to obtain the properties of the multi-layered ground configuration satisfy following expression for the lateral wave: the following inequality relationship:   2 (1) 2 −iµ0k X Z A(λ)γ1 exp (iγ0(z + d)) H (λr) λ  q 0 1 dλ ≤ 2 − ≤ + nπ li ki k0 (n 1) πs. (12) 4π  q (λ) γ0  j 0 To support propagation of trapped surface waves, a dielectric s − 3 2 layer should have a thickness at least half wavelength. The µ0k0 1 ik0 γ1A(k0) ≈ exp (ik0R2 − ip) F(p) integrand in (10) can be without any pole if the suspended 2 πk0r dq(λ) γ0 dλ dielectric layer is too thin. This means that there will not be λ=k0 any significant contribution of energy to the receiving end due (14)

Z   iµ0k0 X A (λ) −1 (1) 2 − exp (iγ0 (z + d)) γ H (λr) λ dλ 4π 6 q (λ) 0 1 k k   q  q   + 2 − 2 2 2 − 2 (1)   A (λk ) exp i (z d) k0 λk λk k1 λk H1 (λk r)   X   2πi q  − 2  dq(λ) 2 2  iµ0k0  k k − λ  = dλ = 0 k (11) 4π λ λk  Z + (1) 2   X A (λ) γ1 exp (iγ0 (z d)) H1 (λr) λ   + dλ   q (λ) γ   j 0   0j 

21876 VOLUME 5, 2017 L. W. Liu et al.: Wireless Energy Harvesting by Direct Voltage Multiplication on Lateral Waves

 2 2 + 2   γ20k1 γ30k2 i γ20k3 tan (γ20l2) A (k ) +γ k2 tan (γ l ) γ k2 − iγ k2 tan (γ l ) 0 = 10 2 10 2 20 3 30 2 20 2  4 2 2 2 2 2  (15a) dq(λ) −k0k tan (γ10l1) −k k tan (γ10l2) + k k tan (γ20l2) + iγ20γ30k γ0 dλ 1 0 3 2 3 2 λ=k0 + 2 2 2 − 2  γ10k0k1 k2 γ20k3 iγ30k2 tan (γ20l20)

(15a), as shown at the top of this page, defines the last fraction by capacitors C1-C4. All the diodes used in this circuit are of (14). In equation (14), F(p) is the Fresnel integral: assumed to be the same and all the discrete capacitors used 1 Z p exp (it) in the circuit are assumed to have a capacitance C. If the F (p) = (1 + i) − √ dt (15b) parasitic inductance L is sufficiently small, then the output 2 p 0 2πt voltage can be derived and approximated using the approach with given in Appendix I into the following [21]: 2       + ik2γ A (k ) nKT 4πqVD 2nKT qIS k0r z d 0 1 0 Vout = 10VD − ln + ln p =  +  (15c) q nKT q nCfnKT 2  r dq(λ)  dλ (16) λ=k0

IV. HARVESTING ENERGY FROM LATERAL WAVES BY where n is the intrinsic ideality of the diode. Is is the reverse DIRECT VOLTAGE MULTIPLICATION saturation current of each of the diodes. nKT/q is the threshold In one of Tesla’s lectures [18], Tesla has highlighted the voltage, which is typical 25 mV at room temperature. f is the fact that power transmission by one-wire operating frequency. The formula given in (16) assumes that is equivalent to wireless power transfer. Although the link the load resistance is infinitely large. The last term of (16) between power transfer by one wire and wireless power also accounts for the frequency dependent effects due to the transmission has not been well explored in other research capacitances in the layout. literature, it was found in a recently published work [21] that The prototypes for the proposed open-ended voltage mul- the energy from a time-varying electromagnetic field can be tiplier have been fabricated on a Rogers Duroid (TM) sub- captured by a one wire transmission without any antenna. strate 4350B with thickness=1.52mm. Fig. 2 shows the In this work, wireless energy is harvested from lateral waves details of the proposed open-ended voltage multiplier. The on the surface of a suspended dielectric layer using a lit- diodes used for fabricating prototypes in this work were tle known open-ended voltage multiplier. Fig. 1 illustrates SMS7630-093 from Skyworks. The schematic diagram, the schematic diagram of the open-ended voltage multiplier the photo of the fabricated prototype and the simulated elec- similar to the one proposed in [21]. This open-ended volt- tric field distribution at 1.24 GHz are respectively shown age multiplier has an input terminated by an open-circuited in Figs. 2a, 2b and 2c. Goubau line. Goubau line is one-wire transmission line hav- The input impedance of the opened voltage multiplier ing characteristic impedance very close to the characteristic was approximately 400 ohm according to electromagnetic impedance of free space. If the end of the Goubau is left open- simulation. It should be noted that, for the purpose of veri- circuited, it becomes a monopole antenna which captures fying the design against the simulation, the output voltages ambient electromagnetic field right on the top surface of the of the proposed voltage multipliers were first measured as suspended dielectric layer without any other form of antenna. a function of frequency when the input terminals were fed The voltage sensed by the Goubau line is rectified into a with a 50 ohm power source (E8267D, Agilent DC voltage using the well-known Avremenko’s diode con- Technologies) at 20 dBm. The measured results together figuration formed by diodes D1 and D2 [22], [23]. The with the results of layout/schematic co-simulation done using voltages across D1 and D2 are very limited because each of Keysight’s Momentum are shown in Fig. 2d. the diodes has its own maximum forward voltage. However, before reaching the output, the voltages across D1 and D2 V. SIMULATED AND MEASURED RESULTS OF can undergo voltage multiplication by the differential voltage BASIC WPT CONFIGURATION multiplier formed by diodes D3, D4, D5 and capacitances C1, The feasibility of wireless power transfer based on the pro- C2, C3 and C4. posed voltage multipliers has been explored using the exper- The output voltage is the sum of the voltages of all the imental configurations as shown in Figs 3a and 3b. Fig 3a diodes D1-D6. The fundamental AC voltage across D1 and illustrates an experimental configuration where the trans- D2, 2VD, depends on the time-varying electromagnetic field mitted energy is expected to be primarily a lateral wave. captured by the Goubau line, which cannot be changed Fig 3b shows an experimental configuration focusing on by changing the circuit topology. However, the AC voltage space waves only. In either configuration, the transmitting across each of all other diodes D3-D6 can be force-increased end is mounted with a base-fed monopole antenna formed to a maximum of 2VD by introducing the AC shorts formed by a planar Goubau line, and the receiving end is vertically

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FIGURE 2. The proposed open-ended voltage multiplier loaded with a FIGURE 3. Experiments on wireless energy harvesting at 640 MHz: 450 ohm resistor: a) the schematic diagram; b) the fabricated circuit. a) Configuration A: with lateral waves and space waves involved. c) Electric distribution simulated on the layout using Keysight’s b) Configuration B: with space waves involved only. c) Measured output Momentum. d) Output voltage as a function of frequency when the input voltage as a function of distance for configurations A and B; d) Simulated is terminated with 50 ohm instead of being left open-circuited. at the receiving end as a function of distance configurations A and B. mounted with the proposed open-ended voltage multiplier In addition to the above measurement, the experimental terminated with a 1 M load resistor. The measured results configurations as shown in Figs. 3a and 3b have been modeled of this work are shown in Fig. 3c. according to (1)-(15). The model, which has been coded in

21878 VOLUME 5, 2017 L. W. Liu et al.: Wireless Energy Harvesting by Direct Voltage Multiplication on Lateral Waves

MATLAB TM, has been used to simulate these experiments. The simulation results are shown in Fig. 3d. The table top was a layer of dry wood covered with a thin layer of plastic coating. The relative and the conductivity of dry wood are respectively 2.1 and 1e-14 S/m. The relative permittivity and the conductivity of the plastic cover are respectively 3 and 1e-16 S/m. The legs of the table are made with steel. The table top is 1m away from the ground, which is another imperfectly conducting plane. The ground is made with steel-reinforced concrete. The dielectric constant of concrete is known to be approxi- mately 5. However, because of the presence of steel bars in the concrete floor and steel legs of the table, the equivalent conductivity of the air underneath the table should not be assumed to be zero. For the purpose of analysis, an equiv- alent conductivity of air underneath the table top has been estimated by experiment. By measurement at different fre- quencies, we have estimated that the equivalent conductivity of air underneath the table top is about 1e-18 S/m. The model given by (1-16) has been coded in MATLAB TM. The parameters used to simulate the magnetic component of the lateral wave are:

ε0 = 8.85e − 12, µ0 = 4πe − 7, f = 640MHz,

ε1 = 2.8, σ1 = 1e − 16, ε2 = 2.1,

σ2 = 1e − 14, ε3 = 1, σ3 = 1e − 18,

l1 = 0.0005m, l2 = 0.015m. It can be observed from Figs 3c and 3d that the harvested energy at the receiving end is much higher in the presence of a lateral wave. In this work, the amplitude of the magnetic field FIGURE 4. Configuration C: Cascading open-ended voltage multipliers for due to the trapped surface wave was too small to be plotted. wireless energy harvesting. a) Experimental configuration; and b) Measured results when spacing between two voltage multipliers is 5cm spacing and when spacing between two voltage multipliers is 10cm. VI. CASCADING OPEN-ENDED VOLTAGE MULTIPLIERS IN SERIES Whilst the energy that can be harvested at a single observation VII. SUGGESTED APPLICATIONS OF point is highly limited, the results of our investigation reveal LATERAL-WAVE-BASED WPT IN AREAS OF that multiple pieces of the proposed open-ended voltage WIRELESS COMMUNICATION multiplier can be connected in series to boost the overall Many research efforts have been devoted to incorporating the efficiency. This means that we can have a number of serially technology of WPT into the existing communication devices, connected open-ended voltage multipliers spanning an area in which surface waves including the above-mentioned lateral to take advantage of every antinode of a lateral wave. waves are definitely applicable. Since space waves and sur- It was found from another experiment as shown face waves differ not only in terms of transmission efficiency, in Fig. 4 that the total output voltage was maximized when but also in terms of mode of propagation, they can potentially each two neighboring pieces of the open-ended voltage mul- be applied differently in the areas of wireless communication. tiplier are spaced at exactly half of the free-space wavelength In the following we introduce some conventional applications apart. In this experimental configuration, the source at the in the field of wireless communication where surface waves transmitting end was powered at 20dBm, 1.24 GHz. At the can be potentially useful. Also, an attempt to present poten- receiving end, two identical open-ended voltage multipliers tial applications in which surface waves might prove to be connected in series were spaced at two different distances: promising. 5cm and 10 cm, corresponding to 1/4 λ and 1/2 λ. The measured results were curved fit and shown in Fig. 4b. It can A. WIRELESS SENSOR NETWORK (WSNs) be observed that the output voltage becomes higher at all In wireless sensor networks (WSNs), a set of sensor nodes are frequencies if two open-ended voltage multipliers cascaded positioned in a specific area for collecting measurements of series are spaced at 1/2 λ. environmental parameters such as temperature, pressure, etc.

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These measurements are then sent to a base station for fur- ther processing. A major limitation of WSNs is that the lifetime of sensors’ batteries is short, and thus they need to be recharged periodically. To that end, the WPT technology is utilized by which a mobile charging vehicle is typically used to charge all sensor nodes wirelessly [24]. In particular, conventional radio-frequency based WPT technique such as inductive or resonance coupling is commonly used for that task; however, it suffers from the low-power efficiency due to the fact that, the harvested power scales inversely with the square of transmission distance, and also causes reduction FIGURE 5. Example system integrating wireless communication and in wireless throughput due to RF interferences as power wireless power transfer together. RF signal is usually much stronger than the low-power data signal. Since lateral waves can significantly increase the energy In practice, conventional monopole antennas can simulta- efficiency due to less signal attenuation compared with space neously handle more than one signals at different frequencies. waves, therefore, WPT based on lateral waves can be used for The power can be preferably delivered at a lower frequency, simultaneous charging of the sensor nodes more efficiently say at any frequency below 500 MHz, where a highly con- without causing harmful interference to wireless communica- centrated lateral wave is easier to form. The signal to be tions. In addition to inherent nature of lateral waves for inter- transmitted can be a conventional WIFI signal or a signal at ference reduction, the delivered power by lateral waves can a much higher frequency. To ensure the delivered power does also be conveyed on a lower frequency channel. In some sce- not impose any interference to the received signal, the energy narios where sensor nodes are deployed in partially or hardly to be processed by the receiver at the receiving end can be pre- accessible environment, RF based WPT becomes challeng- filtered with a high pass filter. Fig. 5 illustrates this scenario. ing. In such scenarios, the mobile charging vehicle may not be able to get close enough to sensor nodes or the existence C. NLOS CHARGING OF A BLACK BOX FOR A of some physical obstacles renders power transfer highly DISAPPEARED FLIGHT inefficient or impossible. Thus, application of WPT based In the aftermath of the recent disappearance of passenger on lateral wave can be potentially very useful and promising, flight MH370 [26], the World Radiocommunication Confer- due to high-power transmission efficiency and the ability for ence (WRC-15) has reached an agreement to allocate the complete interference avoidance. existing frequency band 1087.7-101092.3 MHz for passenger flights to the aeronautical mobile-satellite service (- B. SIMULTANEOUS WIRELESS INFORMATION to-space) so that reception by space stations of Automatic AND POWER TRANSFER (SWIPT) Dependent Surveillance-Broadcast (ADS-B) emissions from Another application of WPT is a scenario in which a source the aircraft is possible. This extension obviously performs simultaneous transmission of wireless information allows ADS-B signals to be transmitted beyond line-of-sight and power to the destination nodes. However, there is always to facilitate reporting the position of missing aircraft equipped a tradeoff between harvested energy and delivered through- with ADS-B anywhere in the world. Whilst this extension put, where many techniques in literature have been developed will undoubtedly enhance the safety in skies, many disap- to achieve that. For instance, time switching and power split- peared flights failed to be tracked down after some months, ting techniques, where data-power signal is split in time and mainly because of one reason; the black box or the flight data power domains, respectively [25]. Undoubtedly, the strength recorder (FDR) of the disappeared flight has simply run out of superimposed data-power signal is usually strong, which of battery power. contributes to interference on other wireless communications FDR is an electronic device mounted in the rear part of as well as health risks. With a surface wave, however, these almost all passenger flights. It records what happens inside concerns can be totally eliminated. the aircraft just before an air accident in order to facili- Motivated by the technique of power line carrier commu- tate a crash investigation. Inside the FDR, there is a device nication (PLCC), both the power and the data signals for known as underwater locator (ULB) which is sup- communication can be superimposed at different frequencies. posed to be powered by a lithium battery and not normally As such, WPT based on lateral waves can be combined with switched on in the absence of any accident. Once the ULB frequency splitting technique in PLCC. It is possible to simul- becomes immersed into , it is activated by a built-in taneously transmit power and deliver data. The composite ‘‘water switch’’ and sends out its ultrasonic 10ms pulse once signal can be transmitted through the wall, the table top, per second at 37.5 kHz. These ultrasonic pulses are normally the surface of ocean or the oxide layer coating any dielectric detectable 1–2 km away from water surface through space object in the form of multiple lateral waves in the absence of waves. In order for the ULB to operate as normal, the battery any radiation loss. voltage must be in the range between 2.97 V and 3.5 V.

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However, the battery power is sufficient for at most three were found to be counterproductive in many of our WPT months after the activation. experiments. Incorporating a solar charger into the ULB design is one Whilst the energy that can be harvested from a single obser- of the ways to maintain continuous operation of the ULB. vation point is limited, the experimental results as shown In most air accidents, however, a disappeared flight usually in Fig. 4b suggest that wireless energy can be harvested from ends up falling directly onto an area where natural light is not more than one observation points as long as the spacing always available. Lateral waves together with trapped surface between two neighboring voltage multipliers are kept at half waves tend to follow the contour of the earth surface. It should of the wavelength. This result suggests that the open-ended come as no surprise that the FDR can also be equipped with a voltage multiplier can form a unit element of a rectanna wireless energy harvester in much the same way as discussed array spanning an area so that more wireless energy can be in Section V. Theoretically, it is possible to remotely power harvested. or charge up the FDR of a misfortune aircraft through a According to the results of our investigation, trapped sur- lateral wave along the surface of the ocean bed or the ground, face waves are nowhere close to be a dominant propagation especially after the battery has run out. This feasibility will mode in far field. In almost all our experiments involving guarantee an uninterrupted tracking of ADS-B signal by the a thin dielectric layer in a stratified ground, the attenuation aeronautical mobile-satellite service. of a typical trapped surface wave was found to be substan- If keeping the battery of an ULB/FDR alive becomes a real- tially higher than that of the associated lateral wave. This is ity, it should be equally possible in future to utilize so-called possibly because of the fact that trapped surface waves have a lateral-wave radar to perform non-line-of-sight tracking of to go through a much longer attenuated pathway than lateral a disappeared flight or other hidden objects. What we need is waves. Lateral wave is guided by total internal reflection on to ground a highly directional monopole antenna with a beam the lower and upper interfaces of a dielectric layer, which is scanning capability in the transmitting end. indeed a less attenuated pathway which bypasses free space. In addition, to support propagation of a trapped surface wave, VIII. DISCUSSIONS the dielectric thickness should be greater than half of the The simulations and experimental results of this work can wavelength. If a dielectric layer is excessively thin, however, be straightforwardly concluded with two observations: a) the trapped surface wave cannot by virtue exist but the intrinsic transmission efficiency of a wireless power can be signifi- conductivity of dielectric layer will force the evanescent elec- cantly improved in the presence of a lateral wave; and b) the tromagnetic waves to propagate as a lateral wave in a highly energy from lateral waves or space waves can be harvested confined volume, with a current density substantially higher by the proposed open-ended voltage multiplier. More impor- than that of a space wave. There is no reason why one cannot tantly, the measured voltage is about 3 volts across the whole take advantage of the lateral wave from stratified ground to transmission range, suggesting that the proposed approach in improve the yield of a wirelessly harvested energy. this work can be used to wirelessly charge up a cell phones In contrast with the conclusions drawn by some other or other similar electronic appliances within 1 m away from studies, the conductivity of this suspended dielectric layer the transmitting source. does not have to be very high in order for a lateral wave to The attenuation in configuration A obtained from our propagate efficiently along the air-dielectric interface. measurement as shown in Fig. 3c is 8.394 dB/m, whilst the Whilst free space is undoubtedly an acceptable medium simulated attenuation according to Fig. 4 is 8.82b dB/m. The for short range WPT, there remain many problems which simulation results roughly agree with the measurement in cannot be solved by space waves alone. On the other hands, terms of attenuation although the shapes of both graphs are there remain many unexplored applications of lateral waves slightly different. in the field of wireless communication. SWIPT and remote The measured voltage against distance for configuration charging of a black box for a disappeared flight are just A was found to be slightly sinusoidal over a long distance, examples of those. The area of WPT based on lateral waves whilst this effect is not obvious in the simulated magnetic warrants more research for betterment of humanity. field as shown in Fig. 4. This slight inconsistency is due to the fact that the model for space wave given in (6a) and (6b) IX. CONCLUSIONS was based on an assumption that the monopole antennas at the In this work, a model for the electromagnetic fields of a strat- transmitting and receiving ends are electrically small. This ified ground with an imperfectly conducting bottom plane assumption is not always valid, particularly for near field has been developed and used to simulate lateral waves prop- analysis. agating along the interface between air and a dielectric layer On the other hand, both experimental and simulated suspended in mid-air. The presence of a lateral wave has been results as shown in Figs 3c and 4 suggest that space waves experimentally verified in a configuration involving a thin alone are far too attenuated to support realistic transmis- table top. A wireless energy has been successfully harvested sion of wireless energy. Most of our simulation results by direct voltage multiplication on a lateral wave, which suggest that the amplitude of the total magnetic field is has outperformed the space wave according to the prediction lower than that of the lateral wave. In fact, space waves by the model. The device proposed for this direct voltage

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Integrating both sides of (A3) yields:

V cos(π+ϕ) c   C Z Vc cos (ωt + ϕ) exp dVc cos (ωt + ϕ) τ VT Vc cos(0+ϕ) τ/2 1 V − I R Z V cos (ωt) = exp dc D exp ac dωt 2π VT VT 0 τ/2 FIGURE 6. Circuit template for derivation of input/output relationship of   1 Z Vc cos (ωt + ϕ) the proposed open-ended voltage multiplier. − (Is − Ix ) exp dωt. (A5) 2π VT 0 multiplication is an open-ended voltage multiplier with an Assuming the capacitance C is sufficiently large so that the open-circuited Goubau line to capture ambient electromag- AC voltage across the capacitance can be ignored, we can netic field and with an output in the form of an enormously ignore the last term of (A4). The last term of (A4) involves Ix , multiplied voltage. The simulated amplitude of the magnetic which is the current leaking to other undisclosed parts of the field at the receiving end was found to be inversely propor- circuit. This assumption means if the capacitance C is large tional to square root of the distance between the enough, other parts of the circuit are NOT expected to affect and the receiver. The simulation results were found to be in the voltage of the diode to a significant extent. good agreement with the experimental outcome in terms of The two integral terms on the right side of (A4) can be attenuation. treated as modified Bessel integrals of the first kind. With this mind, and with the assumption on the value of C, expression APPENDIX in (A4) can be simplified into: Assume that we have a nonlinear circuit containing a voltage       CVT Vc cos(ϕ) Vdc − IDR Vac source, a diode, a capacitor and a load resistor connected in exp ≈ exp I0 . τ V V V series as shown in Fig. 6. The voltage source contains a series T T T (A6) cascade of a DC voltage Vdc and an AC voltage Vaccos(ωt), where ω is the angular frequency in radian per second. The With some algebraic arrangement, the DC voltage across the current in a diode is given as (A1): capacitor as shown in Fig. 6 can be expressed:  V      I = I exp D − 1 (A1) 1 Vac s V Vc cos (ϕ) ≈ Vdc − IDR + VT ln I0 . (A7) T CfVT VT where IS is the reverse saturation current, VT is the threshold Therefore, the rectified voltage across diode can be expressed voltage given by: as: nKT    VT = (A2) Vac q VD ≈ −VT ln I0 + ln (CfVT ) (A8) VT n is the ideality factor and KT/q = 26mV at room temperature. where Io[...] is operator of the Bessel function of the first (A1) ignores the effect of the reverse breakdown voltage kind. In the schematic diagram as shown in Fig. 2a, the input which can lead to an unpredictable decrease in the rectifica- of the circuit is a single-wire transmission line with a char- tion efficiency of the proposed open-ended voltage multiplier. acteristic impedance anywhere between 200 and 550. (A1) can be rewritten according to the circuit information The electromagnetic energy in vicinity of the single-wire given in Fig. 6 as: transmission line is captured into a transverse magnetic mode     dVc cos (ωt + φ) VD (TM mode) which is then rectified into a DC voltage by Avre- IC = C = Is exp −1 + Ix (A3) dt VT menko’s diode configuration formed by diodes D1 and D2. D1 D2 where V and V are respectively the voltages across the However, the voltage across diodes and is not a C D pure DC voltage. They carry AC harmonics which are multi- capacitor and the diode in time domain. VD in (2) can be substituted with V = V + V − V − I R, so that the plied by the differential voltage multiplication process due to D dc ac c D D3 D6 C C following expression is obtained: diodes - and capacitors 1- 4. Capacitors C1-C4 serve as an AC short connected in a dV cos (ωt + φ) C c manner to make sure the AC voltage across each of the diodes dt D1-D4 is maximized to approximately 2 V (t). Since (A8)     D Vdc +Vac cos(ωt)−Vc cos(ωt)−IDR relates the rectified voltage to the AC source, we can use = Is exp −1 +Ix VT the same formula as a template to derive the rectified voltage (A4) across diodes D3, D4, D5 and D6 in terms of the AC voltages

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across diodes D1and D2. Therefore, the voltage output of the [23] L. W. Y. Liu, S. Ge, Q. Zhang, and Y. Chen, ‘‘Capturing surface electro- circuit as shown in Fig. 2a can be expressed as: magnetic energy into a DC through single-conductor transmission line at microwave frequencies,’’ Prog. Electromagn. Res. M, vol. 54, pp. 29–36,    Jan. 2017. 2VD(t) Vout ≈ +2VD + 4VT ln I0 − 4 ln (CfVT ). [24] L. Xie, Y. Shi, Y. T. Hou, and A. Lou, ‘‘Wireless power transfer and VT applications to sensor networks,’’ IEEE Wireless Commun., vol. 20, no. 4, (A9) pp. 140–145, Aug. 2013. [25] R. Zhang and C. K. Ho, ‘‘MIMO broadcasting for simultaneous wireless information and power transfer,’’ IEEE Trans. Wireless Commun., vol. 12, Equation (A9) can be approximated using the Bessel approx- no. 5, pp. 1989–2001, May 2013. imation formula into (A10): [26] M. A. Mujeebu, ‘‘The disappearance of MH370 and the search     operations—The role of technology and emerging research challenges,’’ nKT 4πqV 2nKT qI IEEE Aerosp. Electron. Syst. Mag. V = 10V − ln D + ln S . , vol. 31, no. 3, pp. 6–16, Mar. 2016. out D q nKT q nCfnKT [27] N. Tesla, ‘‘The transmission of electrical energy without wires as a means for furthering peace,’’ Elect. World Eng., pp. 21–24, Jan. 1905. (A10) [28] R. W. P. King and S. S. Sandler, ‘‘The electromagnetic field of a vertical electric dipole in the presence of a three-layered region,’’ Radio Sci., REFERENCES vol. 29, pp. 97–113, Jan./Feb. 1994. [29] R. E. Collin, ‘‘Some observations about the near zone electric field of [1] G. Marconi, Wireless Telegraphic Communication: Nobel Lecture, Dec. 11, a hertzian dipole above a lossy earth,’’ IEEE Trans. Antennas Propag., 1909, Nobel Lectures, 1901-1921. Amsterdam, The Netherlands: vol. 52, no. 11, pp. 3133–3137, Nov. 2004. Elsevier, 1967. [30] R. E. 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Commun., vol. 430, no. 2, neering from Nanyang Technological University, pp. 470–475, Jan. 2013. [20] K. Li, Electromagnetic Fields in Stratified Media. Hangzhou, China: Singapore, in 2011. From 2011 to 2013, he was Zhejiang Univ. Press, 2009. with the Poly-Grames Research Center, Ecole [21] L. W. Liu, A. Kandwal, Z. E. Eremenko, and Q. Zhang, ‘‘Open-ended Polytechnique de Montreal, Montreal, Canada, voltage multipliers for wireless transmission of electric power,’’ J. Microw. as a Post-Doctoral Fellow. Since 2013, he has been Power Electromagn. Energy, vol. 25, no. 3, pp. 187–204, Aug. 2017. with the Southern University of Science and Tech- [22] N. E. Zaev, S. V.Avramenko, and V.N. Lisin, ‘‘Messen des Leitungsstroms, nology, Shenzhen, China as an Assistant Professor. His research interests are die Polarisation des erregten Strom,’’ Russian J. Phys. Gedanken, no. 2, focused on emerging novel electromagnetics technologies and multidisplin- 1991. inary topics.

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YIFAN CHEN received the B.Eng. (Hons.) and MOHAMMED A. TEETI received the Ph.D. Ph.D. degrees in electrical and electronic engi- degree in electrical engineering from the neering from Nanyang Technological University Huazhong University of Science and Technology, in 2002 and 2006, respectively. From 2005 to Wuhan, China, in 2015. He is currently a Post- 2007, he was a Project Officer and then a Doctoral Fellow with the Department of Electronic Research Fellow with the Singapore-University and Electrical Engineering, Southern University of Washington Alliance in bioengineering, sup- of Science and Technology, Shenzhen, China. ported by the Singapore Agency for Science, His current research interests are in the fields of Technology and Research, Nanyang Technologi- wireless communications and information theory, cal University, Singapore, and the University of with focus on massive MIMO, mmWave massive Washington at Seattle, USA. From 2007 to 2012, he was a Lecturer and MIMO, and interference channels. then a Senior Lecturer with the University of Greenwich and Newcastle University, U.K. From 2012 to 2016, he was a Professor and the Head of RANJAN DAS received B.E. degree in electronics Department of Electrical and Electronic Engineering, Southern University of and instrumentation engineering from Jadavpur Science and Technology, Shenzhen, China, appointed through the Recruit- University, and the master’s degree with special- ment Program of Global Experts—the Thousand Talents Plan. In 2013, ization in electronics systems design from the he was a Visiting Professor with the Singapore University of Technology and Electrical Engineering Department, IIT Bombay, Design, Singapore. He is currently with the University of Waikato, Hamilton, where he currently pursuing the Ph.D. degree. New Zealand, as a Professor of Engineering and the Associate Dean External He joined the Electronics and Electrical Engineer- Engagement of the Faculty of Science and Engineering and the Faculty of ing Department, South University of Science and Computing and Mathematical Sciences, University of Waikato, Hamilton, Technology of China, Shenzhen, China, as a Visit- New Zealand. ing Student. His research area includes reconfig- urable multiband filter design, synthesis of negative group delay circuits. He is also interested in real time analog signal processing for microwave frequencies.

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